Markov approximation for controlled Hawkes Jump-Diffusions with general kernels

Mahmoud Khabou; Mehdi Talbi

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arXiv · 2507.11294

Markov approximation for controlled Hawkes Jump-Diffusions with general kernels

Mahmoud Khabou·Mehdi Talbi

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Abstract

We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by a linear combination of exponential functions. This implies that Hawkes jump-diffusions can be approximated with Markov jump-diffusions. We illustrate the usefulness of this approximation by applying it to a class of stochastic control problems.

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BibTeX RIS

Mahmoud Khabou, Mehdi Talbi. 2025-07-15. Markov approximation for controlled Hawkes Jump-Diffusions with general kernels. https://arxiv.org/abs/2507.11294

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